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Lie groups, Calabi-Yau threefolds, and F-theory

Publication ,  Journal Article
Aspinwall, PS; Katz, S; Morrison, DR
Published in: Advances in Theoretical and Mathematical Physics
January 1, 2000

The F-theory vacuum constructed from an elliptic Calabi-Yau threefold with section yields an effective six-dimensional theory. The Lie algebra of the gauge sector of this theory and its representation on the space of massless hypermultiplets are shown to be determined by the intersection theory of the homology of the Calabi-Yau threefold. (Similar statements hold for M-theory and the type IIA string compactified on the threefold, where there is also a dependence on the expectation values of the Ramond-Ramond fields.) We describe general rules for computing the hypermultiplet spectrum of any F-theory vacuum, including vacua with non-simply-laced gauge groups. The case of monodromy acting on a curve of Aeven singularities is shown to be particularly interesting and leads to some unexpected rules for how 2-branes are allowed to wrap certain 2-cycles. We also review the peculiar numerical predictions for the geometry of elliptic Calabi-Yau threefolds with section which arise from anomaly cancellation in six dimensions.

Duke Scholars

Published In

Advances in Theoretical and Mathematical Physics

DOI

EISSN

1095-0753

ISSN

1095-0761

Publication Date

January 1, 2000

Volume

4

Issue

1

Start / End Page

95 / 126

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
 

Citation

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ICMJE
MLA
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Aspinwall, P. S., Katz, S., & Morrison, D. R. (2000). Lie groups, Calabi-Yau threefolds, and F-theory. Advances in Theoretical and Mathematical Physics, 4(1), 95–126. https://doi.org/10.4310/atmp.2000.v4.n1.a2
Aspinwall, P. S., S. Katz, and D. R. Morrison. “Lie groups, Calabi-Yau threefolds, and F-theory.” Advances in Theoretical and Mathematical Physics 4, no. 1 (January 1, 2000): 95–126. https://doi.org/10.4310/atmp.2000.v4.n1.a2.
Aspinwall PS, Katz S, Morrison DR. Lie groups, Calabi-Yau threefolds, and F-theory. Advances in Theoretical and Mathematical Physics. 2000 Jan 1;4(1):95–126.
Aspinwall, P. S., et al. “Lie groups, Calabi-Yau threefolds, and F-theory.” Advances in Theoretical and Mathematical Physics, vol. 4, no. 1, Jan. 2000, pp. 95–126. Scopus, doi:10.4310/atmp.2000.v4.n1.a2.
Aspinwall PS, Katz S, Morrison DR. Lie groups, Calabi-Yau threefolds, and F-theory. Advances in Theoretical and Mathematical Physics. 2000 Jan 1;4(1):95–126.

Published In

Advances in Theoretical and Mathematical Physics

DOI

EISSN

1095-0753

ISSN

1095-0761

Publication Date

January 1, 2000

Volume

4

Issue

1

Start / End Page

95 / 126

Related Subject Headings

  • Nuclear & Particles Physics
  • 5107 Particle and high energy physics
  • 4902 Mathematical physics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics